Objective Knowledge

A Realist View of Logic, Physics, and History (1966)

MAN, some modern philosophers tell us, is alienated from his world:
he is a stranger and afraid in a world he never made. Perhaps
he is; yet so are animals, and even plants. They too were born,
long ago, into a physico-chemical world, a world they never made.
But although they did not make their world, these living things
changed it beyond all recognition and, indeed, remade the small
corner of the universe into which they were born. Perhaps the
greatest of these changes was made by the plants. They radically
transformed the chemical composition of the earth's whole atmosphere.
Next in magnitude are perhaps the achievements of some marine
animals which built coral reefs and islands and mountain ranges
of limestone. Last came man, who for a long time did not change
his environment in any remarkable way, apart from contributing,
by deforestation, to the spread of the desert. Of course, he
did build a few pyramids; but only during the last century or
so , did he begin to compete with the reef-building corals. Still
more recently he began to undo the work of the plants by slightly,
though significantly, raising the carbon dioxide content of the
atmosphere.

Thus, we have not made our world. So far we have not even changed
it much, compared with the changes achieved by animals and plants.
Yet we have created a new kind of product or artefact which promises
in time to work changes in our corner of the world as great as
those worked by our predecessors, the oxygen-producing plants,
or the island-building corals. These new products, which are
decidedly of our own making, are our myths, our ideas, and especially
our scientific theories: theories about the world we live in.

I suggest that we may look upon these myths, these ideas and theories,
as some of the most characteristic products of human activity.
Like tools, they are organs evolving outside our skins. They
are exosomatic artefacts. Thus we may count among these characteristic
products especially what is called 'human knowledge'; where we
take the word 'knowledge' in the objective or impersonal sense,
in which it may be said to be contained in a book; or stored in
a library; or taught in a university.

When referring to human knowledge, I shall usually have this objective
sense of the word 'knowledge' in mind. This allows us to think
of knowledge produced by men as analogous to the honey produced
by bees: the honey is made by bees, stored by bees, and consumed
by bees; and the individual bee which consumes honey will not,
in general, consume only the bit it has produced itself: honey
is also consumed by the drones which have not produced any at
all (not to mention that stored treasure of honey which the bees
may lose to bears or beekeepers). It is also interesting to note
that, in order to keep up its powers to produce more honey, each
working bee has to consume honey, some of it usually produced
by other bees.

All this holds, by and large, with slight differences, for oxygen-producing
plants and for theory-producing men: we, too, are not only producers
but consumers of theories; and we have to consume other people's
theories, and sometimes perhaps our own, if we are to go on producing.

'To consume' means here, first of all, 'to digest', as in the
case of the bees. But it means more: our consumption of theories,
whether those produced by other people or by ourselves, also means
criticising them, changing them, and often even demolishing them,
in order to replace them by better ones.

All these are operations which are necessary for the growthof our knowledge; and I again mean here, of course, knowledge
in the objective sense.

I suggest that it looks at present as if it is this growth of
human knowledge, the growth of our theories, which turns out,
human history into a chapter so radically new in the history
of the universe, and also in the history of life on earth.

All three of these histories-the history of the universe, the
history of life on earth, and the history of man and of the growth
of his knowledge-are, of course, themselves chapters of our knowledge.
Consequently, the last of these chapters-that is, the history
of knowledge-will consist of knowledge about knowledge. It will
have to contain, at least implicitly, theories about theories,
and especially theories about the way in which theories grow.

I shall, therefore, before going any further into my topic, present
a general tetradic schema which I have found more and more useful
as a description of the growth of theories. It is as follows:

P1 » TT » EE » P2.

Here 'P' stands for 'problem'; 'TT' stands for 'tentative
theory'; and 'EE' stands for '(attempted) error-elimination',
especially by way of critical discussion. My tetradic schema
is an attempt to show that the result of criticism, or of error-elimination,
applied to a tentative theory, is as a rule the emergence of
a new problem; or, indeed, of several new problems. Problems,
after they have been solved and their solutions properly examined,
tend to beget problem-children: new problems, often of greater
depth and ever greater fertility than the old ones. 'This can
be seen especially in the physical sciences; and I suggest that
we can best gauge the progress made in any science by the distance
in depth and expectedness between P1 and P2: the best tentative
theories (and all theories are tentative are those which give
rise to the deepest and most unexpected problems.

My tetradic schema can be elaborated in various ways; for example,
by writing it as follows:

» TTa » EEa » P2a

P1 » TTb » EEb » P2b

» TTn » EEn » P2n

In this form the schema would indicate that, if we can, we should
propose many theories as attempts to solve some given problem,
and that we should critically examine each of our tentative solutions.
We then find that each gives rise to new problems; and we may
follow up those which promise the most novel and most interesting
new problem: if the new problem,
P2b, say, turns out to be merely the old P, in disguise,
then we say that our theory only manages to shift the problem
a little; and in some cases we may take this as a decisive
objection to the tentative theory, TTb.

This shows that error-elimination is only part of our critical
discussion: our critical discussion of the competing tentative
theories may compare them, and assess them, from many different
points of view. The decisive point is, of course, always:
how well does our theory solve its problems; that is, P1.

At any rate, one of the things we wish to achieve is to learn
something new. According to our schema, progressiveness is one
of the things we demand of a good tentative theory: and it is
brought out by the critical discussion of it: the theory is progressive
if our discussion shows that it has really made adeference
to the problem we wanted to solve; that is, if the newly emerging
problems are different from the old ones.

If the newly emerging problems are different then we can hope
to learn a great many new things when we proceed to solve them
in turn.

Thus my tetradic schema can be used to describe the emergence
of new problems and, consequently, the emergence of new solutions-that
is, new theories; and I even want to present it as an attempt
to make sense of the admittedly vague idea of emergence-as an
attempt to speak of emergence in a rational manner. I should
like to mention that it can be applied not only to the emergence
of new scientific problems and, consequently, new scientific theories,
but to the emergence of new forms of behaviour, and even new forms
of living organisms.

Let me give you an example. P1 may be, say, a certain problem
concerning the survival of a species, such as the problem of reproduction,
of producing offspring. According to Darwin, this survival problem
has found a good solution if the species survives; any other tentative
solution will be eliminated by the disappearance of both the solution
and the species.

According to my schema, the attempted error-elimination, that
is, the struggle for survival-will bring out the inherent weakness
of each of the proposed solutions in the form of a new problem.
For example, the new problem may be that the parent organisms
and their offspring are threatening to suffocate one another.
This new problem may in turn be solved; for example, the organisms
may develop a method of scattering or disseminating their offspring;
or else the new problem may be solved by the establishment of
a common economy, comprising several organisms. Perhaps the transition
from unicellular to multicellular organisms proceeded in this
way.

However this may be, my schema shows that there may be more than
Darwin's alternative, 'survive or perish', inherent in
the process of error-elimination: error-elimination may bring
out new emerging problems, specifically related to the old problem
and to the tentative solution.

In what follows I shall use my schema, sometimes only implicitly;
and I shall refer to emergence, assuming that my schema makes
this idea sufficiently respectable within what I hope will be
a rational discussion. I propose to deal with some aspects of
the growth of knowledge under four headings:

1. Realism and Pluralism: Reduction versus Emergence

Man produces not only scientific theories but many other ideas
- for example, religious or poetical myths or, say, plots for
stories.

What is the characteristic difference between a scientific theory
and a work of fiction? It is not, I hold, that the theory is
possibly true while the descriptions in the story are not true,
although truth and falsity have something to do with it. The
difference is, I suggest, that the theory and the story are embedded
in different critical traditions. They are meant to be "judged
by quite different traditional standards (even though these standards
may have something in common).

What characterises the theory is that it is offered as a solution
to a scientific problem; that is, either a problem that has arisen
before, in the critical discussion of earlier tentative theories,
or (perhaps) a problem discovered by the author of the theory
now offered, but discovered within the realm of the problems I
and solutions belonging to the scientific tradition.

However, I am not leaving it at that. For the scientific tradition
in its turn is, or was until recently, characterised by what may
be called scientific realism. That is to say, it was inspired
by the ideal of finding true solutions to its problems:
solutions which corresponded to the facts.

This regulative ideal of finding theories which correspond to
the facts is what makes the scientific tradition a realist tradition:
it distinguishes between the world of our theories and the world
of facts to which these theories belong.

Moreover, the natural sciences with their critical methods of
problem solving, and some of the social sciences too, especially
history and economics, have represented for quite a long time
our best efforts in problem solving and fact finding (by fact
finding I mean, of course, the discovery of statements or theories
which correspond to facts). Thus these sciences contain, by and
large, the best statements and theories from the point of view
of truth; that is, those giving the best description of the world
of facts, or of what one calls 'reality'.

Now let us look at certain relations that hold between some of
these sciences.

Take physics and chemistry for example; sciences which make assertions
about all physical things and physical states, including living
organisms.

Physics and chemistry are not very different, and there seems
to be no great difference in the kind of things to which they
apply, except that chemistry, as it is usually understood, becomes
inapplicable at very high temperatures and also, perhaps, at very
low ones. It therefore would not be very surprising if the hopes,
held for a long time, that chemistry can be reduced to physics,
were to come true, as indeed they seem to be doing.

Here we have a real paradigm case of a 'reduction'; by
a reduction I mean, of course, that all the findings of
chemistry can be fully explained by (that is to say, deduced from)
the principles of physics.

Although such a reduction would not be very surprising, it would
be a very great scientific success. It would not only be an exercise
in unification, but a real advance in understanding the world.

Let us assume that this reduction has been carried out completely.
This might give us some hope that we may also reduce one day
all the biological sciences to physics.

Now this would be a spectacular success, far greater than the
reduction of chemistry to physics. Why? Because the kind of
things to which physics and chemistry apply are really very similar
from the start. Only think how difficult it would be to say whether
the atomic theory is a physical or a chemical theory. In fact,
for a long time it was both; and it is this common bond which
provides the link which may lead, or perhaps has led, to their
unification.

With living organisms the situation is different. They are, no
doubt, subject to all kinds of physical and biological laws.
Yet there appears to be some prima facie difference between living
organisms and non-living things. Admittedly, we learn from science
that there are transitory or intermediate stages, and also intermediate
systems; and this gives us hope that a reduction might be achieved
one day. Moreover, it seems not at all improbable that recent
tentative theories about the origin of life on earth might be
successfully put to the test, and that we might be able to create
primitive living organisms artificially.

But even this would not necessarily mean a complete reduction.
This is shown by the fact that chemists were able to create all
sorts of chemicals, inorganic and organic, before understanding
even their chemical composition, to say nothing about their physical
structure. Thus even the control of chemical processes by purely
physical means is not as such equivalent to a reduction of chemistry
to physics. Reduction means much more. It means theoretical
understanding: the theoretical penetration of the new
field by the old field.

Thus we might find a recipe for creating some primitive forms
of life from non-living matter without understanding, theoretically,
what we were doing. Admittedly, this would be a tremendous encouragement
to all those who seek for a reduction, and rightly so. But the
way to a reduction might still be long; and we could not know
whether it was not even impassable: there may be no theoretical
reduction of biology to physics, just as there seems to be neither
a theoretical reduction of mechanics to electrodynamics, nor a
theoretical reduction the other way round.

If the situation is such that, on the one hand, living organisms
may originate by a natural process from non-living systems, and
that, on the other hand, there is no complete theoretical understanding
of life possible in physical terms, then we might speak of life
as an emergent property of physical bodies, or of matter.

Now I want to make it quite clear that as a rationalist I wish
and hope to understand the world and that I wish and hope for
a reduction. At the same time, I think it quite likely that there
may be no reduction possible; it is conceivable that life is an
emergent property of physical bodies.

My point here is that those believers in reduction who, for some
philosophical or other reason, adopt a priori the dogmatic
position that reduction must be possible, in a way destroy their
triumph should reduction ever be achieved. For what will then
be achieved ought to have been achieved all the time; so their
triumph will be only the uninteresting one of having been proved
right by events.

Only those who assert that the question cannot be settled a
priori can claim that any successful reduction would be a
tremendous discovery.

I have dwelt on this point so long because it has some bearing
on the position of the next rung of the ladder-the emergence of
consciousness.

There are philosophers, called 'radical behaviourists' or 'physicalists',
who think that they have a priori reasons, such as Ockham's
razor, for asserting that our introspection of mental states
or events, and our reports about mental states or events, are
simply introspections and reports about ourselves qua physical
systems: they are reports about physical states of these systems.

Two philosophers expected here this morning have defended such
a view with brilliant arguments. They are Herbert Feigl and Willard
Van Orman Quine. I should like to make a few critical remarks
about their views.

Quine says, with a reference to Carnap and Feigl, that if theoretical
progress can be 'achieved by ... positing distinctive mental states
... behind physical behaviour, surely as much ... could be achieved
by positing..... certain correlative physiological states and
events instead.... Lack of a detailed physiological explanation
of the states is scarcely an objection to acknowledging them as
states of human bodies.... The bodily states exist anyway; why
add the others?'

Let me point out that Quine speaks here as a realist: 'The bodily
states exist anyway', he says. Nevertheless, from the point of
view I am adopting here, he is not what I should call a 'scientific
realist': he does not wait to see whether science will achieve
a reduction here, as perhaps it may one day; instead he applies
Ockham's razor, pointing out that mental entities are
not necessary for the theory.

But who knows what Ockham or anybody else might mean here by necessity?
If mental entities or, better, mental states should exist - and
I myself do not doubt that they do exist, then positing mental
states is necessary for any true explanation of them; and should
they one day be reduced to physical states, hen this will be a
tremendous success. But there will be no success at all if we
reject their existence by merely noting that we can explain things
without them, by the simple method of confining ourselves to physical
things and their behaviour.

To sum up my argument in brief: philosophical speculations of
a materialistic or physicalistic character are very interesting,
and may even be able to point the way to a successful scientific
eduction. But they should be frankly tentative theories (as think
Feigl's theories are). Some physicalists do not, however, consider
their theories as tentative, but as proposals to express everything
in a physicalistic language; and they think these proposals have
much in their favour because they are undoubtedly convenient:
inconvenient problems such as the body-mind problem do indeed,
most conveniently, disappear. So these physicalists think that
there can be no doubt that these problems should be eliminated
as pseudo-problems.

To this I would reply that by the same method we could have eliminated
a priori all chemical states and problems connected with
them: we could have said that they were obviously physical, and
that there was no need to specify them in detail: that all we
needed to do was to postulate the existence of some physical state
correlative to each chemical state. : I think it is clear that
the general adoption of such a proposal would have led to the
attitude of not looking for the detailed reduction of chemistry
to physics. No doubt, it would have dissolved the analogue of
the body-mind problem-the problem of the relation of physics to
chemistry; but the solution would have been linguistic; and as
a consequence we should not have learned anything about the real
world.

All this leads me to assert that realism should be at least tentatively
pluralistic, and that realists should subscribe to the following
pluralistic postulate:

We must beware of solving, or dissolving, factual problems

linguistically; that is, by the all too simple method of refusing
to talk about them. On the contrary, we must be pluralists, at
least to start with: we should first emphasise the difficulties,
even if they look insoluble, as the body-mind problem may look
to some.

If we can then reduce or eliminate some entities by way of scientific
reduction, let us do so by all means, and be proud of the gain
in understanding.

So I would say: let us work out in every case the arguments for
emergence in detail, at any rate before attempting reduction.

To sum up and sharpen the considerations advanced in this section:

The reduction of chemistry to physics, apparently now well on
the way, may be described as a paradigm case of a genuine scientific
reduction which satisfies all the requirements of a good scientific
explanation.

'Good' or 'scientific' reduction is a process in which we learn
much that is of great importance: we learn to understand and to
explain the theories about the field to be reduced (in this case
chemistry) and we learn a great deal about the power of the reducing
theories (in this case physics).

It is conceivable, although not yet certain, that the reduction
of chemistry to physics will be completely successful. It is
also conceivable, though less likely, that we may one day have
good reductions of biology, including physiology, to physics,
and of psychology to physiology, and thus to physics.

I call bad reduction or ad hoc reduction the method of
reduction by merely linguistic devices; for example, the method
of physicalism which suggests that we postulate ad hoc the
existence of physiological states to explain behaviour which we
previously explained by postulating (though not by postulating
ad hoc) mental states. Or in other words, by the linguistic
device of saying that I report on a physiological state
of mine when I report that I now feel that I understand the Schrödinger
equation.

This second kind of reduction or the use of Ockham's razor is
bad, because it prevents us from seeing the problem. In ,the
picturesque as well as hard-hitting terminology of Imre Lakatos,
it is a disastrous case of a 'degenerating problem shift';
and it may prevent either a good reduction, or the study of emergence,
or both.

In order to avoid this disastrous method we must in each case
try to learn as much as possible about the field which we hope
to reduce. It may be that the field resists reduction; and we
may even possess arguments to show why the field cannot be reduced.
In this case we may have an example of genuine emergence.

If I may perhaps end my comments on the degenerating of behaviourism
(especially linguistic behaviourism) with the following remark.

Behaviourists and materialists are anti-idealists: and they are,
rightly, opponents of Berkeley's 'esse = percipi' or

to be = to be observable.

According to them, 'to be' is 'to be material', 'to behave as
a body in space and time'. Nevertheless, it may be said that
they do adhere, unconsciously, to Berkeley's equation, although
they put it in a slightly different verbal form:

to be = to be observed

or perhaps

to be = to be perceived.

For they say that only those things exist which can be observed.
They do not realise that all observation involvesinterpretation
in the light of theories, and that what they call 'observable'
is what is observable in the light of pretty old-fashioned and
primitive theories. Though I am all for common sense, I am also
for enlarging the realm of common sense by learning from science.
At any rate, it is not science but dubious philosophy (or
outdated science) which leads to idealism, phenomenalism, positivism;
or to materialism and behaviourism, or to any other of anti-pluralism.

2. Pluralism and emergence in History

I shall not speak about the history of the universe, but only
say a few words about the history of life on earth.

It seems that a very promising start has recently been made towards
reconstructing the conditions under which life emerged
on earth; and I think we may, perhaps, expect some major success
soon. But while sanguine about emergence, even experimental emergence,
I feel very sceptically inclined about reduction. This is due
to certain thoughts of mine about the evolution of life.

It seems to me that evolutionary processes or major evolutionary
changes are as unpredictable as historical processes or major
historical changes. I hold this view because I am strongly inclined
towards an indeterminist view of the world, somewhat more radical
than Heisenberg's: my indeterminism includes the thesis that even
classical physics is indeterministic, and is thus more like that
of Charles Sanders Peirce, or that of Alfred Landé. And
I think that evolution proceeds largely probabilistically, under
constantly changing conditions or problem situations, and that
every tentative solution, whether more successful or less successful
or even completely unsuccessful, creates a new problem situation.
This seems to me to prevent a complete reduction as well as a
complete understanding of the processes of life, although it does
not prevent constant and far-reaching progress towards such understanding.
(This argument should not be taken to be like Bohr's application
of his idea of complementarity to living organisms - an argument
which seems to me very weak indeed.)

But I want to speak in this section mainly about human history,
about the story of mankind. This, as I have indicated, is very
largely the history of our knowledge - of our theories about the
world - and, of course, of the repercussions of these products,
which are of our own making, upon ourselves and our further productions.

It is obvious that one can adopt a physicalist or materialist
attitude towards these theoretical products of ours; and it might
be suspected that my emphasis upon the objective sense of knowledge
- my emphasis upon theories as contained in books collected in
libraries and as taught in universities-indicates that I sympathise
with the physicalist or materialist interpretation of theories;
I mean an interpretation which sees language as consisting of
physical objects - noises, or printed letters-and which sees ourselves
as conditioned, or dispositioned, to react to these noises or
letters with certain characteristic kinds of physical behaviour.

But nothing is further from my intention than to encourage ad
hoc reductions of this kind. Admittedly, if forced to choose
between any subjectivist or personalist view of human knowledge
and the materialist or physicalist view I have just tried to sketch,
I should choose the latter; but this is emphatically not the
alternative.

The history of ideas teaches us very clearly that ideas emerge
in logical or, if the term is preferred, in dialectical contexts.
My various schemata such as

P1 » TT » EE » P2

may indeed be looked upon as improvements and rationalisations
of the Hegelian dialectical schema: they are rationalisations
because they operate entirely within the classical logical organon
of rational criticism, which is based upon the so-called law of
contradiction; that is to say, upon the demand that contradictions,
whenever we discover them, must be eliminated. Critical error-elimination
on the scientific level proceeds by way of a conscious search
for contradictions.

Thus history, and especially the history of ideas, teaches us
that if we want to understand history, we must understand ideas
and their objective logical (or dialectical) relationships.

I do not believe that anybody who has ever seriously gone into
any chapter of the history of ideas will think that a reduction
of these ideas could ever be successful. But I take it as my
task here not so much to argue against the possibility of any
reduction, as to argue for the recognition of emergent entities,
and for the need to recognise and describe these emergent entia
before one can seriously think about their possible elimination
by way of reduction.

One of my main arguments for the emergent character of theories
I have given elsewhere. My argument depends upon the conjecture
that there is such a thing as a genuine growth of scientific knowledge;
or in practical terms, that tomorrow, or a year hence, we may
propose and test important theories of which nobody has seriously
thought so far. If there is growth of knowledge in this sense,
then it cannot be predictable by scientific means. For he who
could so predict today by scientific means our discoveries of
tomorrow could make them today; which would mean that there would
be an end to the growth of knowledge.

On the other hand, unpredictability in principle has always been
considered as the salient point of emergence; and it seems to
me that my argument shows at any rate that the growth of knowledge
must be unpredictable in principle.

But there are other arguments for the emergent character of theories,
or of knowledge in the objective sense. I shall only mention
an argument or two against the very popular and very naive view
that theories can be reduced to the mental states of those who
produce them, or of those who understand them. (Whether or not
these mental states themselves may then perhaps be reduced to
physical states in turn will not be further discussed.)

The idea that a theory in its objective or logical sense may be
reduced to the mental states of those who hold the theory takes,
as a rule, the form that the theory just is a thought.
But this is a trivial mistake: it is the failure to distinguish
between two senses of the word 'thought'. In its subjective sense,
the word 'thought' describes a mental experience or a mental process.
But two mental experiences or processes, though they may stand
in causal relations to each other, cannot stand in logical relations
to each other.

Thus, if I say that certain ideas of the Buddha agree with certain
ideas of Schopenhauer, or that they contradict certain ideas of
Nietzsche, then I am not speaking about the mental thought-processes
of these people or about their interrelations. If I say, however,
that Nietzsche was influenced by certain ideas of Schopenhauer,
then I do mean that certain thought processes of Nietzsche's were
causally influenced by his reading of Schopenhauer. So we have
actually these two different worlds, the world of thought-processes,
and the world of the products of thought-processes.
While the former may stand in causal relationships, the
latter stand in logical relationships.

The fact that certain theories are incompatible is a logical fact,
and holds quite independently of whether or not anybody has noticed
or understood this incompatibility. These purely objective logical
relationships are characteristic of the entities which I have
called theories, or knowledge, in the objective sense.

This may also be seen from the fact that the person who produces
a theory may very often not understand it. Thus it might be argued
without paradox that Erwin Schrödinger did not fully understand
the Schrödinger equation, at any rate not until Max Born
gave his statistical interpretation of it; or that Kepler's area
law was not properly understood by Kepler, who seems to have disliked
it.

In fact, understanding a theory is something like an infinite
task, so that we may well say that a theory is never fully understood,
even though some people may understand some theories extremely
well. Understanding a theory has, indeed, much in common with
understanding a human personality. We may know or understand
a man's system of dispositions pretty well; that is to say, we
may be able to predict how he would act in a number of different
situations. But since there are infinitely many possible situations,
of infinite variety, a full understanding of a man's dispositions
does not seem to be possible. Theories are similar: a full understanding
of a theory would mean understanding all its logical consequences.
But these are infinite in a non-trivial sense: there are infinitely
many situations of infinite variety to which the theory might
be applicable; that is to say, upon which some of its logical
consequences may bear; and many of these situations have never
been thought of; their possibility may not yet have been discovered.
But this means that nobody, neither its creator nor anybody who
has tried to grasp it, can have a full understanding of all the
possibilities inherent in a theory; which shows again that the
theory, in its logical sense, is something objective and something
objectively existing - an object that we can study, something that
we try to grasp. It is no more paradoxical to say that theories
or ideas are our products and yet not fully understood by us than
to say that our children are our products and yet not fully understood
by us, or that honey is a product of the bee, yet not fully understood
by any bee.

Thus, the study of the history of our theories or ideas-and a
good case could be made for the view that all human history is
largely a history of our theories or ideas-should make us all
pluralists. For what exist, for the historian, are people in
physical, social, mental, and ideological problem situations;
people producing ideas by which they try to solve these problems,
ideas which they try to grasp, to criticise, to develop.

The student of the history of ideas will find that ideas have
a kind of life (this is a metaphor, of course); that they can
be misunderstood, rejected, and forgotten; that they can reassert
themselves, and come to life again. Without metaphor, however,
we can say that they are not identical with any man's thought,
or belief; that they can exist even if universally misunderstood,
and rejected.

All this may be reminiscent of Plato and Hegel. But there are
great differences here. Plato's 'ideas' were eternal, unchanging
conceptions or notions; Hegel's were dialectically self-changing
conceptions or notions. The ideas which I find most important
are not conceptions or notions at all. They correspond not to
words but to statements or propositions.

In opposition to Plato and Hegel I consider tentative theories
about the world-that is, hypotheses together with their logical
consequences-as the most important citizens of the world of ideas;
and I do not think (as Plato did) that their strangely non-temporal
character makes them eternal and thereby more real than
things that are generated and are subject to change, and to decay.
On the contrary, a thing that can change and perish should for
this very reason be accepted as prima facie real; and even an
illusion is, qua illusion, a real illusion.

This is important in connection with the problem of time, and
of change.

A historian cannot, I think, accept the doctrine that time and
change are illusions; a doctrine upheld by some great physicists
and philosophers such as Parmenides, Weyl, and Schrödinger.
Nothing is more real than an event, an occurrence; and every
event involves some change.

That the pluralistic universe in which the historian lives, with
its individual men living individual lives, trying to solve their
problems, producing children, and ideas about them, hoping and
fearing and deceiving themselves and others, but always theorising,
and often seeking not only happiness but also truth-that this
pluralistic universe should be successfully 'reduced' to one or
another kind of monism-this seems to me not only unlikely, but
impossible. But this is not my point here. My point is that
only after recognising the plurality of what there is in this
world can we seriously begin to apply Ockham's razor. To invert
a beautiful formulation of Quine's, only if Plato's beard is sufficiently
tough, and tangled by many entities, can it be worth our while
to use Ockham's razor. That the razor's edge will be dulled in
being used for this tough job is only to be expected. The job
will no doubt be painful. But it is all in a day's work.

3. Realism and Subjectivism in Physics

There are two important fields in modern physics in which physicists
have allowed subjectivism not only to enter, but to play an essential
role: Boltzmann's theory of the subjectivity of the direction
of time, and Heisenberg's interpretation of the indeterminacy
formulae as determining a lower limit to the effect of the observer's
interference with the observed object.

There was also another intrusion of the subject, or of the observer,
w hen Einstein brought in the observer in a number of imaginary
thought experiments intended to elucidate relativity; but this
is a field from which the observer was exorcised, slowly but steadily,
by Einstein himself.

I shall not discuss this point further, nor shall I discuss the
subjective theory of time which, in trying to tell us that time
and change are human illusions, forgets that they are very real
illusions which have in no way been reduced to anything else (and
which, I conjecture, are not amenable to reduction). I shall
not discuss all this because I have done so only recently. I
merely want to say a few words about the Heisenberg formulae and
their interpretation.

These formulae are usually derived in a fairly complicated manner;
there is, for example, an interesting derivation by Weyl and another
rather complicated one by Born.

Yet in fact the Heisenberg formula for energy depends neither
on wave mechanics nor on Heisenberg's matrix mechanics; nor do
we need the commutation relations (which according to Hills are
insufficient for the derivation of the formulae). It simply does
not depend on the revolutionary new quantum mechanics of 1925-6,
but follows directly from Planck's old quantum postulate of 1900:

E = hf.

From this we get immediately

(2) DE = h Df.

By using the principle of harmonic resolving power,

(3) Df approx = 1/Dt,

we obtain from (2) and (3)

(4) DE approx = h / Dt,

which leads at once to

(5) DE . Dt approx = h;

that is to say, a form of Heisenberg's so-called indeterminacyformulae.

In precisely the same way we obtain the Heisenberg formula for
position and momentum from Duane's principle (whose analogy to
Planck's principle has recently been stressed by Alfred Landé).
It may be written

(6) Dpi approx = h / Dqi

According to Landé this may be interpreted as follows:
a body (such as a grid or a crystal) endowed with the space-periodicity
Dqi is entitled to change its momentum pi in
multiples of Dpi approx = h / Dqi.

From (6) we obtain at once

(7) Dpi . Dqi approx = h,

which is another form of Heisenberg's indeterminacy formulae.

Considering that Planck's theory is a statistical theory, the
Heisenberg formulae can be most naturally interpreted as statistical
scatter relations, as I proposed more than thirty years
ago. That is, they say nothing about the possible precision of
measurements, nor anything about limits to our knowledge. But
if they are scatter relations, they tell us something about the
limits to the homogeneity of quantum-physical states, and therefore,
though indirectly, about predictability.

For example, the formula Dpi . Dqi approx
= h (which can be obtained from Duane's principle just
as DE . DT approx = h can be obtained
from Planck's principle) tells us, simply, that if we determine
the coordinate x of a system (say, an electron) then, upon
repetition of the experiment, the momentum will scatter.

Now how can such an assertion be tested? By making a long series
of experiments with a fixed shutter opening Dx and
by measuring, in every single case, the momentum Px. If
these momenta scatter as predicted, then the formula has survived
the test. But this shows that in order to test the scatter relations,
we have actually measured, in every case, px with a precision
far greater than Dpx; for otherwise we could not speak
of Dpx, as the scatter of px.

Experiments of the kind described are carried out every day in
all physical laboratories. But they refute Heisenberg's indeterminacy
interpretation, since measurements (though not the predictions
based upon them) are more precise than this interpretation permits.

Heisenberg himself noted that such measurements are possible,
but he said that it was 'a matter of personal belief' or personal
taste' whether or not we attach any meaning to them; and ever
since this remark they have been universally disregarded as meaningless.
But they are not meaningless, for they have a definite function:
they are tests of the very formulae in question; that is, of the
indeterminacy formulae qua scatter relations.

There is, therefore, no reason whatever to accept either Heisenberg's
or Bohr's subjectivist interpretation of quantum mechanics. Quantum
mechanics is a statistical theory because the problems it tries
to solve-spectral intensities, for example -are statistical problems.
There is, therefore, no need here for any philosophical defence
of its non-causal character.

The irreducibility of statistical theories to deterministic theories
(rather than the incompatibility of these two kinds of theories)
should, however, be established. Arguments to this effect have
been offered by Landé, and very different ones by myself.

To sum up, there is no reason whatsoever to doubt the realistic
and objectivistic character of all physics. The role played by
the observing subject in modern physics is in no way different
from the role he played in Newton's dynamics or in Maxwell's theory
of the electric field: the observer is, essentially, the man who
tests the theory. For this, he needs a lot of other theories,
competing theories and auxiliary theories. All this shows that
we are not so much observers as thinkers.

4. Realism in Logic

I am opposed to looking upon logic as a kind of game. I know
about so-called alternative systems of logic and I have actually
invented one myself, but alternative systems of logic can be discussed
from very different points of view. One might think that it is
a matter of choice or convention which logic one adopts. I disagree
with this view.

My theory is briefly this. I look upon logic as the theory of
deduction or of derivability, or whatever one chooses to call
it. Derivability or deduction involves, essentially, the transmissionof truth and the retransmission of falsity: in a valid
inference truth is transmitted from the premises to the conclusion.
This can be used especially in so-called 'proofs'. But falsity
is also retransmitted from the conclusion to (at least) one of
the premises, and this is used in disproofs or reputations, and
especially in critical discussions.

We have premises and a conclusion; and if we show that the conclusion
is false, and assume that the inference is valid, we know that
at least one of our premises must be false. This is how logic
is constantly used in critical discussion, for in a critical discussion
we attempt to show that something is not in order with some assertion.
We attempt to show it; and we may not succeed: criticism may
be validly answered by counter-criticism.

What I should wish to assert is (1) that criticism is a most important
methodological device; and (2) that if you answer criticism by
saying, 'I do not like your logic: your logic may be all right
for you, but I prefer a different logic, and according to my logic
this criticism is not valid', then you may undermine the method
of critical discussion.

Now I should distinguish between two main uses of logic, namely
(1) its use in the demonstrative sciences-that is to say, the
mathematical sciences-and (2) its use in the empirical sciences.

In the demonstrative sciences logic is used in the main for proofs-for
the transmission of truth-while in the empirical sciences it is
almost exclusively used critically-for the retransmission of falsity.
Of course, applied mathematics comes in too, in which we implicitly
make use of the proofs of pure mathematics, but the role of mathematics
in the empirical sciences is somewhat dubious in several respects.
(There exists a wonderful article by Schwartz to this effect.)

Now, what I wish to assert is this. If we want to use logic in
a critical context, then we should use a very strong logic, the
strongest logic, so to speak, which is at our disposal; for we
want our criticism to be severe. In order that the criticism
should be severe we must use the full apparatus; we must use all
the guns we have. Every shot is important. It doesn't matter
if we are over-critical: if we are, we shall be answered by counter-criticism.

Thus we should (in the empirical sciences) use the full or classical
or two-valued logic. If we do not use it but retreat into the
use of some weaker logic - say, the intuitionist logic, or some
three-valued logic (as Reichenbach suggested in connection with
quantum theory)-then, I assert, we are not critical enough; it
is a sign that something is rotten in the state of Denmark (which
in this case is the quantum theory in its Copenhagen interpretation,
as I indicated earlier).

Now let us look, by contrast, at proofs. Every mathematician
knows that considerable interest lies in proving a theorem with
the help of a minimum apparatus. A proof which uses stronger
means than necessary is mathematically unsatisfactory, and it
is always interesting to find the weakest assumptions or minimum
means which have to be used in a proof. In other words, we want
the proof not only to be sufficient - that is to say valid-but
we want it if possible to be necessary, in the sense that a minimum
of assumptions have been used in the proof. This, I admit, is
a somewhat sophisticated view. In unsophisticated mathematics
we are happy and grateful if we can prove anything, but in more
sophisticated mathematics we really want to know what is necessary
for proving a theorem.

So if one can prove mathematical theorems with methods weaker
than the full battery of classical logic, then this is extremely
interesting from a mathematical point of view. Thus in proof
theory we are interested in weakening if possible our classical
logic, and we can, for example, introduce intuitionist logic or
some other weaker logic such as positive logic, and investigate
how far we can get without using the whole battery.

I think, incidentally, that the term 'intuitionist logic' is a
misnomer. It is just a name for a very interesting and somewhat
weakened form of classical logic invented by Brouwer and formalised
by Heyting. I certainly do not want to say anything in favour
of the philosophical theory called intuitionism though I should
like to say something in favour of the Brouwer-Heyting logic.
But I trust it will not be supposed that I am in any sense defending
the authority of intuition in philosophy or logic or anywhere
else. Leaving aside for the moment Brouwerian logic, one might
say that intuitionism is the doctrine that intuitions are not
only important but generally reliable. As against this
I think that intuitions are very important but that as a rule
they do not stand up to criticism. So I am not an intuitionist.
However, Brouwerian or so-called 'intuitionist logic' is, from
the standpoint of the present discussion, important because it
is just a part, a genuine part, and thus a weakened form, of classical
logic; that is to say, every inference which is valid from the
point of view of intuitionist logic is also valid from the point
of view of classical logic, while the opposite s not the case:
we have inferences which may be validly drawn in classical logic
but which are not valid in intuitionist logic. Thus if I can
prove a theorem (so far proved only by classical means) with intuitionist
logic, I have made a real mathematical discovery; for mathematical
discoveries do not consist only in finding new proofs of new theorems,
but they consist also in finding new proofs of old theorems; and
a new proof of a theorem will be especially interesting if it
uses weaker means than the old proof. A proof using stronger
means one can always have for the asking, a fortiori; yet
finding a weaker proof is a real mathematical achievement.

So intuitionistic logic is a very interesting approach to mathematics
because it tries to prove as many mathematical theorems as possible
with reduced logical means.

Intuitionistic logic has a further advantage: one can show that
in it the so-called 'law of excluded middle' is not demonstrable
(although it is a well-formed formula of the system) One can also
show that if in any system whatsoever some well-formed formula
is not demonstrable, then the system must be consistent. Generally
speaking, the weaker the logical means we use, the less is the
danger of inconsistency the danger that a contradiction is derivable.
So intuitionist logic can also be looked upon as an attempt to
make more certain that our arguments are consistent and that we
do not get into hidden inconsistencies or paradoxes or antinomies.
How safe such a weakened logic is, as such, is a question into
which I do not want to enter now; but obviously it is at least
a little safer than the full classical logic. I do not suppose
it is always safe, but that is not my point. My point is this.
If you wish to prove, or to establish something, you should use
weak means. But for disestablishing it-that is to say, for criticising
it-we may use strong means. Of course someone might say, 'Look
here, I can refute you even with weak means; I do not even need
to use the whole of intuitionist logic.' Still, that is not very
important. The main thing is that for the rationalist any criticism
is welcome-though he may reply to it by criticising the criticism.

Now this rationalist view is a realist view of logic. First,
because it looks upon logic partly in connection with the methodology
of the natural sciences which, I have tried to argue, is a realistic
affair. Secondly, and this is a very special point, because it
looks upon logical inference as truth transmitting or falsity
re-transmitting; that is to say, it is concerned with the idea
of truth.

I would assert that not the least important of the achievements
of Alfred Tarski is that by introducing two ideas into logic,
he has actually made logic very much a realistic affair. The
first is Tarski's idea (partly anticipated by Bolzano) that logical
consequence is truth transmission. The second, I would say, is
the rehabilitation of the correspondence theory of truth, the
rehabilitation of the idea that truth is simply correspondence
with the facts.

I think I may differ here a little from Quine, because I think
that this idea of Tarski's ought to be interpreted as destructive
of relativism, and because I think that Tarski's claim that his
theory of truth is an 'absolutistic' theory of truth is correct.
In order to explain this point, I will recount a very old story
with a slightly new point to it. The old story is the story of
the three main theories of truth. The new point is the elimination
of the word 'truth' from the story, and with it, of the appearance
that we are dealing here with words, or verbal definitions. However,
for this elimination some preparatory discussion is needed.

Of the three main theories of truth, the oldest was the correspondence
theory, the theory that truth is correspondence with the facts,
or to put it more precisely, that a statement is true if (and
only if) it corresponds to the facts, or if it adequately describes
the facts. This is the theory which I think Tarski has rehabilitated.
The second theory is the so-called coherence theory: a statement
is regarded as true if (and only if) it coheres with the rest
of our knowledge. The third theory is that truth is pragmatic
utility or pragmatic usefulness.

Now, the coherence theory has all sorts of versions of which I
shall mention just two. According to the first, truth is coherence
with our beliefs, or more precisely, a given statement is true
if it coheres with the rest of our beliefs. This I find a bit
disconcerting because I do not want to put beliefs into logic,
for well-known reasons. (If Peter believes p, and if p
and q are interdeducible, we might say that Peter is logically
bound to believe q. Yet he may not know that p and
q are interdeducible, and he may in fact disbelieve q.)

According to the second version of the coherence theory a certain
given statement, of which we do not know whether it is true or
not, is to be accepted as true if (and only if) it coheres with
the statements we have previously accepted. This version has
the effect of making our knowledge utterly conservative: 'entrenched'
knowledge can hardly be overthrown.

The theory of pragmatic utility is especially concerned with the
problem of theories in the natural sciences such as physics.
It says that we should accept a physical theory as true if it
turns out in tests, and other applications, to be pragmatically
useful, or successful.

I propose now to use something like a trick. My trick consists
in this. I shall very soon, until very near the end of this paper,
stop referring to truth. I shall not any longer ask, 'What
is truth?' There are several reasons. My main reason is that
I believe that 'What is?' or 'What are?' questions or, in other
words, all verbal or definitional questions, should be eliminated.
'What is?' or 'What are?' questions I regard as pseudo-questions;
they do not all seem to be so pseudo, but I do think they all
are pseudo-questions. Questions such as, 'What is life?' or 'What
is matter?' or 'What is mind?' or 'What is logic?' I think should
not be asked. They are typically unfruitful questions.

So I think we should also discard the question, 'What is truth?'
My first reason (just mentioned) for discarding the question 'What
is truth?' one may call 'anti-essentialism'. My second reason
is even more important. It is that we should altogether avoid,
like the plague, discussing the meaning of words. Discussing
the meaning of words is a favourite game of philosophy, past and
present: philosophers seem to be addicted to the idea that words
and their meaning are important, and are the special concern of
philosophy.

I will for your convenience present again here-on the next page-a
table which I have used before.

On the left we have words or concepts and their meanings, and
on the right we have statements or propositions or theories
and their truth.

IDEASthat is

DESIGNATIONS or TERMSor CONCEPTS

STATEMENTS or PROPOSITIONSor THEORIES

may be formulated in

WORDS

ASSERTIONS

which may be

MEANINGFUL

TRUE

and their

MEANING

TRUTH

May be reduced, by way of

DEFINITIONS

DERIVATIONS

to that of

UNDEFINED CONCEPTS

PRIMITIVE PROPOSITIONS

The attempt to establish (rather than reduce) by these means their

MEANING

TRUTH

leads to an infinite regress

Now I have been taught by the experience of a lifetime in this
field that one should always try to get away from the left side
of the table and to keep to the right side. One should always
keep to assertions, to theories, and the question of their truth.
One should never get involved in verbal questions or questions
of meaning, and never get interested in words. If challenged
by the question of whether a word one uses really means this or
perhaps that, then one should say: 'I don't know, and I am not
interested in meanings; and if you wish, I will gladly accept
your terminology.' This never does any harm. One should never
quarrel about words, and never get involved in questions of terminology.
One should always keep away from discussing concepts. What we
are really interested in, our real problems, are factual problems,
or in other words, problems of theories and their truth. We are
interested in theories and how they stand up to critical discussion;
and our critical discussion is controlled by our interest in truth.

Having said this, I intend now to stop using the word 'truth'.

Our problem is no longer: Is truth correspondence? Is truth coherence?
Is truth usefulness? This being so, how can we formulate our
real problem?

Our problem can be sharply formulated only by pointing out that
the opponents of the correspondence theories all made an assertion.
They all asserted that there cannot be such a thing as the
correspondence between a statement and a fact. This is their
central assertion. They say that this concept is meaningless
(or that it is undefinable, which, incidentally, in my opinion
does not matter, since definitions do not matter) In other words,
the whole problem arises because of doubts, or scepticism, concerning
correspondence: whether there is such a thing as a correspondence
between a statement and a fact. It is quite clear that these
doubts are serious (especially in view of the paradox of the liar).

It is also quite clear that, but for these doubts, the upholders
of the coherence theory and of the theory of pragmatic usefulness
would really have nothing to argue against. Nobody denies that
pragmatic usefulness and such matters as predictive power are
important. But should there exist something like the correspondence
of a theory to the facts, then this would obviously be more
important than mere self-consistency, and certainly also much
more important than coherence with any earlier knowledge' (or
'belief'); for if a theory corresponds to the facts but does not
cohere with some earlier knowledge, then this earlier knowledge
should be discarded.

Similarly, if there exists something like the correspondence of
theory to the facts, then it is clear that a theory which corresponds
to the facts will be as a rule very useful; more useful, qua theory,
than a theory which does not correspond to the facts. (On the
other hand, it may be very useful for a criminal before a court
of justice to cling to a theory which does not correspond to the
facts; but as it is not this kind of usefulness which the
pragmatists have in mind, their views raise a question which is
very awkward for them: I mean the question, 'Useful for whom?'.)

Although I am an opponent of pragmatism as a philosophy of science,
I gladly admit that pragmatism has emphasised something very important:
the question whether a theory has some application, whether it
has, for example, predictive power. Praxis, as I have put
it somewhere, is invaluable for the theoretician as a spur and
at the same time as a bridle: it is a spur because it suggests
new problems to us, and it is a bridle because it may bring us
down to earth and to reality if we get lost in over-abstract theoretical
flights of our imagination. All this is to be admitted. And
yet, it is clear that the pragmatist position will be superseded
by a realist position if we can meaningfully say that a statement,
or a theory, may or may not correspond to the facts.

Thus the correspondence theory does not deny the importance of
the coherence and pragmatist theories, though it does imply that
they are not good enough. On the other hand, the coherence and
pragmatist theories assert the impossibility or meaninglessness
of the correspondence theory.

So without ever mentioning the word 'truth' or asking, 'What does
truth mean?' we can see that the central problem of this whole
discussion is not the verbal problem of defining 'truth' but the
following substantial problem: can there be such a thing as a
statement or a theory which corresponds to the facts, or which
does not correspond to the facts?

Behind the doubts concerning the possibility of speaking about
correspondence, there are various strong arguments.

First of all, there are paradoxes or antinomies which arise out
of this correspondence idea. Secondly, there are the countless
unsuccessful attempts to say more precisely what the correspondence
between a statement and a fact consists of There is the attempt
of Schlick, who said that correspondence is to be explained by
a one-one relationship between the linguistic statement and the
fact; that is, by uniqueness. A statement, he said, is 'true',
or corresponds to the facts, if it stands to the facts of the
world in a one-one relationship or in a unique relationship: non-correspondence
or 'falsity' is the same as ambiguity. Of course, this is an
unacceptable view, for many vague and ambiguous statements (such
as 'there are a few people somewhere in America') may correspond
to the facts; and vice versa, every general proposition or theory
which corresponds to the facts corresponds to many facts, so that
there is not a one-one relationship.

Moreover, a statement which does not correspond to the facts may
be quite unambiguous. A murderer may say unambiguously, 'I have
not killed him.' There is no ambiguity in this assertion; but
it does not correspond to the facts. Clearly, Schlick's attempt
to explain correspondence misfires. Another even worse attempt
is Wittgenstein's. Wittgenstein suggested that a proposition
is a picture of reality and that correspondence is a relationship
very much like the one that holds between the groove on a gramophone
record and the sounds which it denotes: a kind of projective relationship
between facts and statements. The untenability of this view can
easily be shown. One is reminded of the famous story of Livingstone
being introduced by an interpreter to a Negro king whom he asked,
'How are you?'. The Negro king answered with one word, and the
interpreter began to talk and talk and talk and talk, for ten
minutes, translating the word to Livingstone in the form of a
long story of the king's sorrows. Then Livingstone asked whether
the king was in need of medical assistance, and then the king
began to talk and talk and talk and talk and talk. And the interpreter
translated it with one word: 'No.'

No doubt this story is invented. But it is well invented; and
it illustrates the weakness of the projection theory of language,
especially as a theory of the correspondence between a statement
and a fact.

But this is not all. The matter is even more serious; namely,
Wittgenstein, after having formulated this theory, said that it
is impossible to discuss the relationship of language to reality,
or to discuss language at all. (Because language cannot be discussed
by language.) This is a field in which words fail us. 'It shows
itself' is his favourite expression to indicate the failure of
words. Any attempt to go deeper into the relationship between
language and reality or to discuss language more deeply or statements
more deeply is, accordingly, bound to be meaningless. And although
he says in the Preface of his book, 'the truth of the thoughts
that are here set forth seems to me unassailable and definitive',
he ends up by saying, 'Anybody who understands me eventually recognises
them [the propositions of the Tractatus] as nonsensical.'
(Because talk about language is meaningless.) No doubt this refers,
apart from other things, especially to his theory of projection.
His remark that his readers will see that what he says is meaningless
thus confirms what the opponents of the correspondence theory
have always said of the correspondence theory, namely that it
is meaningless to speak about the correspondence between a statement
and a fact.

So we are back at the real issue. It is this: is there or is
there not a tenable correspondence theory? Can we or can we not
speak meaningfully of the correspondence between a statement and
a fact?

Now my assertion is that Tarski has rehabilitated the correspondence
theory. This, I think, is a great achievement, and it is a great
philosophical achievement. I say this because it has been denied
by many philosophers (for example, by Max Black) that there is
something philosophically important in Tarski's achievement.

The key to the rehabilitation of the correspondence theory is
a very simple and obvious observation made by Tarski. That is,
if I want to speak about correspondence between a statement S
and a fact F, then I have to do so in a language in
which I can speak about both: statements such as S, and
facts such as F. This seems to be frightfully trivial;
but it is nevertheless decisive. It means that the language in
which we speak in explaining correspondence must possess the means
needed to refer to statements, and to describe facts.
If I have a language which has both these means at its disposal,
so that it can refer to statements and describe facts, then in
this language -the metalanguage-I can speak about correspondence
between statements and facts without any difficulty, as we shall
see.

A metalanguage is a language in which we talk about some other
language. For example, a grammar of the German language, written
in English, uses English as a metalanguage in order to talk about
German. The language about which we talk in the metalanguage
(in this case English) is usually called the 'object language'
(in this case German). The characteristic thing about a metalanguage
is that it contains (metalinguistic) names of words and
of statements of the object language, and also (metalinguistic)
predicates, such as 'noun (of the object language)' or
'verb (of the object language)' or 'statement (of the object language)'.
If a metalanguage is to suffice for our purpose it must also,
as Tarski points out, contain the usual means necessary to speak
about at least all those facts about which the object language
can speak.

All this is the case if we use English as our metalanguage in
order to speak about German (as the object language under investigation).

For example, we shall be able to say in the English metalanguage
such things as:

The German words 'Das Gras ist grün' form a statement
of the German language.

On the other hand, we shall be able to describe in our (English)
metalanguage the fact which the German statement 'Das Gras
ist grün' describes. We can describe this fact in English
simply by saying that grass is green.

We can now make a statement in the metalanguage about the correspondence
of a statement of the object language to the facts as follows.
We can make the assertion: The German statement'Das
Gras ist grün' corresponds to the facts if, and only if,
grass isgreen. (Or: '. . . only if it is a fact
that grass is green.')

This is very trivial. It is, however, important to realise the
following: in our assertion, the words 'Das Gras ist grün',
put within quotes, function as a metalinguistic (that is,
an English) name of a German statement; on the other hand,
the English words 'grass is green' occur in our assertion above
without any quotation marks: they do not function as a
name of a statement, but simply as the description of a fact
(or alleged fact).

This makes it possible for our assertion to express a relationship
between a (German) statement, and a fact. (The fact
is neither German nor English, although it is, of course, described
or spoken about in our metalanguage, which is English: the fact
is non-linguistic, it is a fact of the real world, although we
need of course a language if we wish to talk about it.) And what
our metalinguistic assertion asserts is that a certain (German)
statement corresponds to a certain fact (a non-linguistic
fact, a fact of the real world) under conditions which are precisely
stated.

We can, of course, replace the German object language by any other-even
by English. Thus we can make the metalinguistic assertion:

The English statement 'Grass is green' corresponds to the facts
if,and only if, grass is green.

This looks even more trivial. But it can hardly be denied; nor
can it be denied that it expresses the conditions under which
a statement corresponds to the facts.

Generally speaking, let 'S' be a (metalinguistic) name
of a statement of the object language, and let 'f' be the
abbreviation of an expression of the metalanguage that
describes the (supposed) fact F which S describes.
Then we can make the following metalinguistic assertion:

A statement S of the object language corresponds to the
facts if, and only if, f. (or: . . . if it is a fact that
f.)

Note that while 'S' is here a metalinguistic name of a
statement, 'f' is not a name, but an abbreviation of an
expression of the metalanguage describing a certain fact (the
fact which we can name 'F').

We can now say that what Tarski did was to discover that in order
to speak about the correspondence between a statement S and a
fact F, we need a language (a metalanguage) in which we
can speak about the statement S and state the fact
F. (The former we speak about by using the name
'S', the latter by using a metalinguistic expression 'f'
which states or describes F.)

The importance of this discovery is that it dispels all doubt
about the meaningfulness of talking about the correspondence of
a statement to some fact or facts.

Once this is done, we can, of course, replace the words corresponds
to the facts' by the words 'is true'.

Tarski, apart from this, introduced a method of giving a definition
of truth (in the sense of the correspondence theory) for any
consistent formalised system. But this is not, I think,
his main achievement. His main achievement is the rehabilitation
of talk about correspondence (and truth). Incidentally, he showed
under what circumstances such talk may lead to paradoxes, and
how we can avoid these paradoxes; and he alsoshowed
how in ordinary talk about truth we can, and do, avoid paradoxes.

Once we have settled that we can use 'truth' in the sense of the
correspondence of statements to facts, there is really nothing
of importance to be added about the word 'truth'. There is no
doubt that correspondence to the facts is what we usually call
'truth'; that in ordinary language it is correspondence that we
call 'truth', rather than coherence or pragmatic usefulness.
A judge who admonishes a witness to speak the truth and nothing
but the truth does not admonish the witness to speak what he thinks
is useful either for himself or for anybody else. The judge admonishes
a witness to speak the truth and nothing but the truth but he
does not say, 'All we require of you is that you do not get involved
in contradictions', which he would say were he a believer in the
coherence theory. But this is not what he demands of the witness.

In other words, the ordinary sense of 'truth' as it is used in
courts of law is, no doubt, correspondence. But my main point
is that this may be regarded as an afterthought, and as an unimportant
afterthought. For if anybody should want to say, 'No, in ordinary
language, "truth" is used in a different sense', I should
not quarrel with him. I should suggest that we forget all about
terminology: I should be prepared to use the terminology of my
opponent, pointing out, however, that we have at least these
three meanings at our disposal: this is the only thing about which
I should be prepared to quarrel; but I should refuse to quarrel
about words.

I should point out, though, that the correspondence theory of
truth is a realistic theory; that is to say, it makes the distinction,
which is a realistic distinction, between a theory and the facts
which the theory describes; and it makes it possible to say that
a theory is true, or false, or that it corresponds to the facts,
thus relating the theory to the facts. It allows us to speak
of a reality different from the theory. This is the main thing;
it is the main point for the realist. The realist wants to have
both a theory and the reality or the facts (don't call it 'reality'
if you don't like it, just call it 'the facts') which are different
from his theory about these facts, and which lie can somehow
or other compare with the facts, in order to find out whether
or not it corresponds to them. Of course, the comparison is always
extremely difficult.

One last word about Tarski's theory. Its whole purpose is often
misinterpreted: it is wrongly assumed that it is intended to yield
a criterion of truth. For-coherence was so intended, and
likewise pragmatic usefulness; they strengthened the traditional
view that any serious theory of truth should present us with a
method of deciding whether or not a given statement is true.

Tarski has proved many things from his definition of truth. Among
other things, he has proved that in a sufficiently powerful language
(and in every language in which we can formulate mathematical
or physical theories) there can be no criterion of truth; that
is, no criterion of correspondence: the question of whether a
proposition is true is not in general decidable for the languages
for which we may form the concept of truth. Thus the concept
of truth plays mainly the role of a regulative idea. It helps
us in our search for truth that we know there is something like
truth or correspondence. It does not give us a means of Finding
truth, or of being sure that we have found it even if we have
found it. So there is no criterion of truth, and we must not
ask for a criterion of truth. We must be content with the fact
that the idea of truth as correspondence to the facts has been
rehabilitated. This has been done by Tarski; and I think that
he has thereby rendered an immense service to the realistic outlook.

Although we have no criterion of truth, and no means of being
even quite sure of the falsity of a theory, it is easier to find
out that a theory is false than to find out that it is true (as
I have explained in detail elsewhere). We have even good reasons
to think that most of our theories-even our best theories are,
strictly speaking, false; for they oversimplify or idealise the
facts. Yet a false conjecture may be nearer or less near to the
truth. Thus we arrive at the idea of nearness to the truth, or
of a better or less good approximation to the truth; that is,
at the idea of 'verisimilitude'. I have tried to show
that this idea can be rehabilitated in a way similar to Tarski's
rehabilitation of the idea of truth as correspondence to the facts.
In order to do so I have used mainly the two Tarskian ideas mentioned
here. One is the idea of truth. The other is the idea of logical
consequence; or more precisely, of the set of logical consequences
of a conjecture, or the content of a conjecture.

By incorporating into logic the idea of verisimilitude or approximation
to truth, we make logic even more 'realistic'. For it can now
be used to speak about the way in which one theory corresponds
better than another to the facts-the facts of the real world.

To sum up. As a realist I look upon logic as the organon ofcriticisms (rather than of proof) in our search for true
and highly informative theories - or at least for new theories
that contain more information, and correspond better to the facts,
than our older theories. And I look upon criticism, in its turn,
as our main instrument in promoting the growth of our knowledge
about the world of facts.